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"In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings, scientists have recognized patterns suggesting that the designers had made a conceptual breakthrough in mathematics beginning as early as the 13th century. A new study shows that the Islamic pattern-making process, far more intricate than the laying of one's bathroom floor, appears to have involved an advanced math of quasi crystals, which was not understood by modern scientists until three decades ago. The findings, reported in the current issue of the journal Science, are a reminder of the sophistication of art, architecture and science long ago in the Islamic culture. They also challenge the assumption that the designers somehow created these elaborate patterns with only a ruler and a compass. Instead, experts say, they may have had other tools and concepts."